Orthogonal polynomials

Combinatorics

Pure mathematics

Classical orthogonal polynomials

Schur's theorem

Mathematics

Logarithm

Gegenbauer polynomials

Mathematical analysis

Schur polynomial

Macdonald polynomials

Discrete orthogonal polynomials

Conjecture

Transactions of the American Mathematical Society

We show that normalized Schur polynomials are strongly log-concave. As a consequence, we obtain Okounkov’s log-concavity conjecture for Littlewood–Richardson coefficients in the special case of Kostka numbers.

Logarithmic concavity of Schur and related polynomials